DATING FOR BAYESIANS: Here's How To Use Statistics To Improve Your Love Life

Tuesday

Nov 5, 2013 at 7:05 PM

Andy Kiersz

I am a somewhat socially awkward person. This sometimes makes first dates a daunting proposition.

People go on dates mainly to see if they click with each other, and to figure out if there is any potential for a liaison or a relationship. Being somewhat awkward, it is not always easy for me to see how these things are going in the moment.

Fortunately, I have math on my side, and a tool that will let me update and re-evaluate the odds that my date is going well, based on the events of the date.

That tool is called Bayes' Theorem.

Bayes' Theorem might be the coolest thing in probability theory. It gives us a way to rigorously combine an initial degree of belief in a proposition A with new evidence E that goes for or against that proposition.

For our purposes of seeing how the date is going, A is going to be the proposition that my date is into me, and E will be various events that happen during the date that will affect my estimate of the likelihood of A.

This post will teach you how to incorporate events that happen during your date into figuring out whether the date is going well and likely to lead to something more.

We're interested in the probability of A, represented as P(A). One way to interpret this probability is as my degree of certainty, measured from 0% to 100%, that A is true — that my date is in fact into me.

We start with a "prior" probability — a baseline, without any particular evidence for or against the proposition, before the date begins, often based on historical observations. In our case here, about one in ten of the first dates I have been on have led to something more , so we'll start with a prior probability of 10%, or 0.1, that my date is into me at the very beginning of the date.

Of course, this prior probability is not overly useful to us. The actual events of the date will give us a much better idea of my date's interest in me. Suppose that we are on a fairly standard first date — meeting up for drinks after work. Suppose further that our initial conversation is going well. We're laughing at each others' jokes, sharing stories of college misdeeds, and making copious eye contact. We now have a piece of evidence, E, that will allow us to update the likelihood of A (the odds that the date is successful).

We want to find the probability that my date is into me, given that the early conversation is going well. We symbolize a conditional probability like this as P(A | E) — recall that A is my date liking me, and E is our new evidence from the good early conversation. We call this updated assessment of the likelihood of our proposition the "posterior probability".

The key to finding this posterior probability is Bayes' theorem, which is the formula below. (Don't worry, we'll explain what all this means):

There's a bunch of symbols and terms in the theorem, so let's take a look at what they all mean:

P(A | E) on the left hand side is, as we said above, the updated likelihood that my date likes me (A), given that we've seen our new evidence (E) — the good early date conversation.

P(A), the prior probability, shows up a couple times on the right hand side of the equation. We saw above that this is our level of belief in the notion that my date likes me, before factoring in the evidence of the lovely early date conversation. We also supposed above that P(A) should be 0.1, or 10%.

P(E | A), also showing up twice on the right hand side of the equation, is the flipside of what we're looking for — the probability that we would see the evidence E, assuming that the proposition A is true. In our example, if we were to assume that my date is into me (A), what is the likelihood of having a good early conversation (E)? This is where the magic of Bayes' theorem lies — it is often much easier to answer this reversed question than it is to answer our original question. In our case, P(E | A) should be reasonably high — if my date is into me, it is pretty likely that my date will enjoy my witty banter. We can estimate this then as saying P(E | A) = 0.8, or 80%.

But there is of course also a chance that the early stages of the date go well, even if there is no chemistry there — my date might be laughing at my jokes out of politeness, or perhaps enjoy my company platonically, without any other spark. We deal with this situation in the lower right corner of the equation.

P(E | not A) is the probability that we see our evidence E, given that the proposition A is not happening. That is, the likelihood of having a lovely early date conversation over drinks, assuming that my date does not feel particularly attracted towards me. We just saw a couple situations where this could be true, so P(E | not A) might be something around 0.3, or 30%.

The last term we need, also down at the bottom right of the Bayes formula, is the prior probability, before considering the new evidence, that my date is not into me: P(not A). We can actually figure out this probability pretty easily. Either my date is into me, or they are not into me — exactly one of these two things has to be true — so the probability my date is into me, P(A), and the probability my date is not into me, P(not A), have to add up to 100%, the probability of anything that we know for sure has to be true. Through the power of arithmetic, this means that P(not A) is just 100% minus P(A), which we supposed above to be 10%, and so P(not A) will be 100% — 10%, giving us 90%, or 0.9.

Putting all of our terms into the Bayes formula, and pulling out our calculator, we get:

We now have the updated posterior probability — 0.23. Factoring in the evidence of a good early conversation, I have more than doubled my level of belief that my date is into me, going from our prior probability of 10% to a posterior probability of 23%, or almost one in four.

An awesome feature of Bayesian inference is that we can repeat this process as we get yet more evidence, using the posterior probability from our last step as the new prior probability. Later on in the date, emboldened by my new, somewhat higher degree of certainty that my date is into me, I lean in for a kiss, and, to my delight, they lean right back. We can use this new evidence, a kiss, just as we did above.

Our prior probability P(A), the level of belief that my date is into me before factoring in the kiss, is now the posterior from our last calculation, 0.23, and as above, P(not A) = 1 — P(A) = 0.77.

Here, P(E | A), the probability that my date kisses me in the case that they like me, is going to be pretty high, perhaps 70%, or 0.7.

Our other case, though, is going to be quite unlikely — it would be a little surprising if my date kisses me but they are not into me, so P(E | not A) will probably be in the realm of just 10%, or 0.1. Again using Bayes' theorem and our calculator, we get a new posterior of:

Because my date kissed me, I'm now a good bit more sure that they are into me. To be precise, I believe it to be 68% likely that the date is going well. Perhaps not quite time to start picking out baby names, but certainly pretty good odds.

Bayes' Theorem is used throughout the sciences, but the underlying principles outlined above — viewing probability as an assessment of how likely something is to be true, and constantly updating that assessment as new evidence emerges — can be a very good outlook to use in everyday life.

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